Deficiency

The deficiency of a Binomial Coefficient ${n+k\choose k}$ with $k\leq n$ is the number of $i$ for which $b_i=1$, where

$$n+i=a_ib_i,$$

$1\leq i\leq k$, the Prime factors of $b_i$ are $>k$, and $\prod a_i=k!$, where $k!$ is the Factorial.

See also Abundance

References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 84-85, 1994.